That would require the tabs to track and compare filenames, which I imagine can be expensive. And also, what if the parent directory also matches with the parent of a different file? With an option like windowTitle (I suggest tabTitle), TextMate doesn't have to make a best guess.
My tabs currently look like this:
<Pasted File.png>Having the same trouble working with JS. Ideally TM could do this automatically.If there are two or more tabs with the same name, then show the directory name too.